Coupled Solutions for Two-Dimensional Decagonal Piezoelectric Quasicrystals with Cracks

With the assistance of Stroh formalism, the general solutions satisfying the basic laws of linear elastic theory are written in complex variable forms. To analyze the fracture behavior of two-dimensional decagonal piezoelectric quasicrystals, an elliptical hole model under different boundary conditions is established. The analytical expressions of generalized stress intensity factors (GSIFs) are obtained, respectively, for four general cases: a Griffith crack with generalized remote uniform loading, arbitrary loading on the crack surface, concentrated loading at any position of the crack surface, and multiple collinear periodic cracks under uniform loading at infinity. Numerical examples are given, and the effects of crack length, loading position, loading condition, and crack period on GSIFs are discussed. The derived analytical solutions of cracks play a significant role in understanding the phonon-phason and electromechanical coupled behavior in quasicrystals, and they also serve as criteria for fracture analysis.